A HYBRID MICROSCOPIC MODEL FOR MULTIMODAL TRAFFIC WITH EMPIRICAL OBSERV ATIONS FROM AERIAL FOOTAGE Georg Anagnostopoulos Corresponding Author

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A HYBRID MICROSCOPIC MODEL FOR MULTIMODAL TRAFFIC WITH

EMPIRICAL OBSERVATIONS FROM AERIAL FOOTAGE

Georg Anagnostopoulos, Corresponding Author

Urban Transport Systems Laboratory (LUTS)

EPFL, Lausanne, Switzerland, CH-1015

georgios.anagnostopoulos@epﬂ.ch

Nikolas Geroliminis, Ph.D.

Urban Transport Systems Laboratory (LUTS)

EPFL, Lausanne, Switzerland, CH-1015

nikolas.geroliminis@epﬂ.ch

Submission Date: October 26, 2022

arXiv:2210.14022v1 [cs.SI] 25 Oct 2022

Anagnostopoulos, Geroliminis 2

ABSTRACT

Microscopic trafﬁc ﬂow models can be distinguished in lane-based or lane-free depending on the

degree of lane-discipline. This distinction holds true only if motorcycles are neglected in lane-

based trafﬁc. In cities, as opposed to highways, this is an oversimpliﬁcation and it would be more

accurate to speak of hybrid situations, where lane discipline can be made mode-dependent. Empir-

ical evidence shows that cars follow the lanes as deﬁned by the infrastructure, while motorcycles

do not necessarily adhere to predeﬁned norms and may participate in self-organized formation

of virtual lanes. This phenomenon is the result of complex interactions between different trafﬁc

participants competing for limited space. In order to better understand the dynamics of modal

interaction microscopically, we ﬁrst analyze empirical data from detailed trajectories obtained by

the pNEUMA experiment and observe patterns of mixed trafﬁc. Then, we propose a hybrid model

for multimodal vehicular trafﬁc. The hybrid model is inspired by the pedestrian ﬂow literature,

featuring collision-free and anticipatory properties, and we demonstrate that it is able to reproduce

empirical observations from aerial footage.

Keywords: Anticipation, Collision-free, Drones, Mixed Trafﬁc, Virtual Lane

Anagnostopoulos, Geroliminis 3

INTRODUCTION

Diversiﬁcation of urban mobility leads to competition of different trafﬁc modes for the limited

road space as deﬁned by the existing infrastructure. Empirical evidence from advanced sensors,

coupled with appropriate trafﬁc ﬂow models can enhance our understanding of complex modal

interactions that cannot be readily described by vehicular trafﬁc theory. Revisiting the traditional

trafﬁc ﬂow models can be also seen as the consequence of empirical evidence from new data

collection methods, such as drone videography.

A fascinating application of drone videography in trafﬁc is the pNEUMA dataset, which

incorporates a massive collection of naturalistic vehicle trajectories captured by a swarm of drones

in the center of Athens, Greece. Details of this experiment along with suggested applications are

discussed in (1). PNEUMA holds the promise of enabling new insights into multi-modal urban

trafﬁc, but at the same time, it also introduces a number of methodological challenges. Most

notably, vehicle positions are not always matched to lanes. A more ﬁne-grained organization of

the data is therefore critical for a wide spectrum of downstream tasks, both on microscopic and

macroscopic levels. We address this issue by formulating and solving a map matching problem

and by introducing a novel methodology for detailed segmentation of vehicle trajectories based on

steering events. As steering events, we deﬁne the critical points in time when a driver changes

steering direction. Prerequisites for the determination of steering events are knowledge of the road

network, matching of vehicles to road segments and information about kinematic characteristics,

such as headings. Observed phenomena, such as lane formation, are then modeled microscopically.

Microscopic trafﬁc ﬂow models can be classiﬁed in two broad categories depending on

the assumption of lane-discipline: lane-based (2–5) and lane-free (6–9). This clear-cut distinction

holds true only if motorcycles are neglected in the ﬁrst case. In urban environments, as opposed to

highways, this is an oversimpliﬁcation and it would be more accurate to speak of hybrid situations

of mode-dependent lane discipline. Motorcycles, or in general powered-two-wheelers (PTW), have

unique kinematic characteristics (10) and their interactions with cars are not yet well understood.

For an extensive review of PTW literature, see (11).

In general, vehicular ﬂow theory does not sufﬁciently cover the PTW case, because even the

most fundamental trafﬁc variables, such as density, are hydrodynamic in nature, whereas PTW has

granular characteristics (12). A more adequate framework can be inspired by research in pedestrian

ﬂow, where experimental results (13–17) reveal striking resemblance to phenomena observed in

PTW trafﬁc and dedicated trafﬁc variables have been developed (18, 19). We distinguish mainly

two kinds of microscopic pedestrian models that have been applied to PTW trafﬁc: discrete choice

and self-driven particle systems. Discrete choice models include the multinomial logit (8, 20, 21)

and the nested logit model (22–24). In particular, (24) investigates the case when ﬂow is dominated

by motorcycles, (20) models a speciﬁc queuing scenario of motorcycles at an intersection based

on lateral position, but without considering their orientation, and (21) models a similar situation

with bicycles. Self-driven particle systems, can be distinguished in ﬁrst order models (25–28),

based on velocity (including heading), and second order models (29, 30), based on acceleration. In

motorized trafﬁc, only second order models have been proposed (6, 31). The potential of ﬁrst order

pedestrian models for modeling PTW movement remains unexplored. These models have several

appealing properties, such as simple formulation, very few parameters, consideration of heading

and are collision-free by construction.

This paper is organized in two parts. The ﬁrst section is dedicated to empirical observations

and data segmentation. The last part introduces the hybrid model for mixed vehicular trafﬁc ﬂow.

Anagnostopoulos, Geroliminis 4

Our main focus is on the investigation, analysis and modeling of complex phenomena of self-

organization, as exempliﬁed by the formation of virtual lanes.

EMPIRICAL OBSERVATIONS AND DATA SEGMENTATION

In order to facilitate a thorough investigation of multi-modality in the pNEUMA dataset, given that

it contains 25% of motorcycles, our objective is to solve the trajectory segmentation problem for

heterogeneous trafﬁc, where lane discipline can be only partially assumed. In fact, it is reasonable

to pose the problem in terms of self-organized lane formation instead of lane discipline. Starting

from a macroscopic segmentation of all the vehicle trajectories, including motorbikes, we are

interested to see, on a microscopic level, which parts of the trajectories are lane-keeping and which

parts are devoted to maneuvering. Then, lanes in the most general sense of lane-keeping envelopes,

can be easily identiﬁed as a direct consequence.

In principle, vehicles never travel in perfectly straight lines and there is always some

amount of curvature present. Lane-keeping requires regular corrections from the driver or rider

who performs the steering. Surprisingly, the frequency of critical steering events drops drastically

during the execution of lane-changing or other maneuvers. There is typically only one steering

correction per maneuver. The existence of this sparsity is the main discovery of this paper and we

will show that it can greatly simplify the challenging task of lane detection. This statement holds if

we assume that the aforementioned critical events can be obtained. Of course, this is not generally

possible or easy as it requires ﬁrst, that vehicle headings are given, and second, that they are also

devoid of noise, especially non-Gaussian anomalies. Very recent research on the pNEUMA dataset

(32), discusses these matters in detail and we will assume for the reminder of the paper that perfect

heading information is available.

Macroscopic trajectory segmentation

Because the pNEUMA dataset comes from an airborne experiment in a large urban area with more

than 100 intersections, matching of vehicles to road segments augments the data with important

contextual information such as road azimuth, trafﬁc signal or bus stop locations. Interestingly,

in (33), the authors postulate that even macroscopic analysis can beneﬁt from map matching by

facilitating the detection and exclusion of parked vehicles. It is known that parked vehicles are not

considered as trafﬁc participants in the sense of the two-ﬂuid theory of town trafﬁc (34).

The most successful method for macroscopic trajectory segmentation is the Hidden Markov

Model (HMM). HMM "is an algorithm that can smoothly integrate noisy data and path constraints

in a principled way" (35). Initially, HMM was used for matching sparse GPS data, so, somewhat

surprisingly, direct application of HMM map matching on dense trajectories from the pNEUMA

dataset is problematic. This is due to the abundance of stationary observations, commonly referred

to as stay points. In urban settings, stay points can be the result of low speeds during congestion,

service related stops, the existence of trafﬁc signals or emergency breaking due to random events.

The static data entries, excluding parked vehicles, in the pNEUMA dataset are typically in the

range of 40% or more, which means that there is a great potential for compression. Consequently,

we proceed as follows: each trajectory is divided in two parts: one static and one moving. This is a

simple form of data reduction. The advantage of this approach is threefold. First, the computational

burden on the HMM algorithm can be reduced. Second, we can now make continuity assumptions

for the moving part. Third, the method is lossless and the two trajectory partitions, static and

moving, can be easily reconciled further downstream.

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AHYBRIDMICROSCOPICMODELFORMULTIMODALTRAFFICWITHEMPIRICALOBSERVATIONSFROMAERIALFOOTAGEGeorgAnagnostopoulos,CorrespondingAuthorUrbanTransportSystemsLaboratory(LUTS)EPFL,Lausanne,Switzerland,CH-1015georgios.anagnostopoulos@ep.chNikolasGeroliminis,Ph.D.UrbanTransportSystemsLaboratory(LUTS)EPFL,Lausanne...

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A HYBRID MICROSCOPIC MODEL FOR MULTIMODAL TRAFFIC WITH EMPIRICAL OBSERV ATIONS FROM AERIAL FOOTAGE Georg Anagnostopoulos Corresponding Author

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